Geography Reference
In-Depth Information
values of u and N the character of the solution is determined by the zonal wave
number k. The streamline patterns corresponding to these cases for westerly flow
are illustrated in Fig. 7.10. In the narrow ridge case (Fig. 7.10a), the maximum
upward displacement occurs at the ridge tops, and the amplitude of the disturbance
decays with height. In the wide ridge case (Fig. 7.10b), the line of maximum upward
displacement tilts back toward the west (m > 0), and amplitude is independent of
height consistent with an internal gravity wave propagating westward relative to
the mean flow.
Alternatively, for fixed zonal wave number and buoyancy frequency the
solution depends only on the speed of the mean zonal wind. As indicated in (7.48),
only for mean zonal wind magnitudes less than the critical value N/k will vertical
wave propagation occur.
Equation (7.46) was
ob
tained for conditions of constant basic state flow. In real-
ity, both the zonal wind u and the stability parameter N generally vary with height,
and ridges are usually isolated rather than periodic. A wide variety of responses
are possible depending on the shape of the terrain and wind and stability profiles.
Under certain conditions, large-amplitude waves can be formed, which may gener-
ate severe downslope surface winds and zones of strong clear air turbulence. Such
circulations are discussed further in Section 9.4.
7.5
GRAVITY WAVES MODIFIED BY ROTATION
Gravity waves with horizontal scales greater than a few hundred kilometers and
periods greater than a few hours are hydrostatic, but they are influenced by the
Coriolis effect and are characterized by parcel oscillations that are elliptical rather
than straight lines as in the pure gravity wave case. This
elliptical polarization
can
be understood qualitatively by observing that the Coriolis effect resists horizontal
parcel displacements in a rotating fluid, but in a manner somewhat different from
that in which the buoyancy force resists vertical parcel displacements in a statically
stable atmosphere. In the latter case the resistive force is opposite to the direction
of parcel displacement, whereas in the former it is at right angles to the horizontal
parcel velocity.
7.5.1
Pure Inertial Oscillations
Section 3.2.3 showed that a parcel put into horizontal motion in a resting atmo-
sphere with constant Coriolis parameter executes a circular trajectory in an anti-
cyclonic sense. A generalization of this type of inertial motion to the case with
a geostrophic mean zonal flow can be derived using a parcel argument similar to
that used for the buoyancy oscillation in Section 2.7.3.
